Abstract: We investigate the dynamics of homogeneous phase space for single-fieldmodels of inflation. Inflationary trajectories are formally attractors in phasespace, but since in practice not all initial conditions lead to them, somedegree of fine tuning is required for successful inflation. We explore how thedynamics of non-canonical inflation, which has additional kinetic terms thatare powers of the kinetic energy, can play a role in ameliorating the initialconditions fine tuning problem. We present a qualitative analysis ofinflationary phase space based on the dynamical behavior of the scalar field.This allows us to construct the flow of trajectories, finding that trajectoriesgenerically decay towards the inflationary solution at a steeper angle fornon-canonical kinetic terms, in comparison to canonical kinetic terms, so thata larger fraction of the initial-conditions space leads to inflation. Thus,non-canonical kinetic terms can be important for removing the initialconditions fine-tuning problem of some small-field inflation models.